Let $f(x) = 3x + 3$ and $g(x) = 4x + 3.$ What is $f(g(f(2)))$?
We first find that $f(2) = 9.$ Therefore, $g(f(2)) = g(9) = 39.$ Finally, $f(g(f(2))) = f(39) = \boxed{120}.$